Student Research

Research

I completed my Ph.D. at UW Madison in 2008. My areas of research are number theory (specifically, arithmetic geometry) and linear algebra (specifically the study of numerical ranges in matrix analysis). My thesis advisor was Jordan Ellenberg.

For more information about my background, see my CV on my homepage (click "Home" in the menu at the top of the screen).

Student Research


Undergraduate Research is defined as "An inquiry or investigation conducted by an undergraduate student that makes an original intellectual or creative contribution to the discipline." (Council on Undergraduate Research). Here at ISU, we are exploring some official channels for bringing undergraduate research opportunities to more students. Some examples of successful programs which I have been involved in are individual Directed Research projects, Honors Theses, Research Weekend, summer NSF-supported REUs, and class taste-of-research experiences via Inquiry-Based Mathematics Education.

This page currently focuses on individual directed research projects.

My past students have presented their work at many internal and external forums in which to share and present their research. Here are a few examples of conferences I have some experience with, where mathematics students can present their research, and to which I may have funding to support your trips:

Why do research?

Research projects are valuable experiences for undergraduate students. For instance, a research project:

  • Enhances student learning through mentoring relationships with faculty

  • Increases retention

  • Increases enrollment in graduate education and provides effective career preparation

  • Develops critical thinking, creativity, problem solving and intellectual independence

  • Develops an understanding of research methodology

  • Promotes an innovation-oriented culture

(cf. CUR)

How to get started?

1. Ask a professor. Some professors have ideas for research projects or directed studies, so visit office hours and ask around. However, advising a student in research takes a lot of time, so be respectful when they decline. Take a look at each professor’s website to get an idea of what topics they are interested in. Some professors have sites specific to working with students, and we may list some links here. Others have specific semesters in which they get many students involved in research.

2. Attend local or online math talks. Sometimes questions discussed in talks can lead to interesting projects. If you go to a face-to-face mathematics talk, such as a colloquium talk, many professors are present so it can also lead to a natural person to work with.

3. Math journals. and competitions One easy type of project to get involved in is to try solving a problem posed in a math journal. For example, you can find current problems from the following journals: Math Horizons, Math Magazine, College Math Journal, American Math Monthly, and the Pi Mu Epsilon Journal. Dr. Rault has access to each of these. These problems can be worked on with other students or even with a professor, and correct solutions submitted by their posted deadlines will be acknowledged in the next issue. Several of Dr. Rault's past students have been cited in these journals (see CV). The annual national Putnam competition can also provide good problems for deeper explorations.

Some recent student research projects. The underlined people were all students!

Expectations of the student:

a. Professionalism. A high level of professionalism is required: do not wait until the last moment to finish tasks, don’t be afraid to ask questions or look things up, come prepared to meetings, don’t waste time, give forewarning if you are going to cancel a meeting, and be sure to dress and act professionally at conferences.

b. Meetings. Most research progress takes place outside of meeting times. However, it is expected that a faculty advisor may ask you to meet for 1 to 3 hours per week, and for you to meet for 1 to 3 hours per week with other student collaborators as well (for a total of about 4 hours of meeting time per week). If one week you are unprepared or overwhelmed with exams, then be sure to cancel the meeting in advance: remember to avoid wasting time. Conversely, it is expected that the student leave extra time aside at high stress times like conference presentations -- expect to start early and meet extra.

c. Agreement to disseminate. Faculty receive credit for doing research when talks or publications arise as a result. Therefore, it is an expectation that, if the faculty advisor deems the project to be of interest to the general mathematics population, the student (i) seek travel funding to attend a conference, (ii) create a talk using LaTeX and practice it under supervision of the faculty advisor, and (iii) help in writing any requested proof details for a paper for publication.

Suggested pre-requisites for extended projects:

Firstly, short projects are very possible without any pre-requisites. For example, seminars and Inquiry-Based Learning experiences can provide a taste-of-research, with many of the benefits described above. As can projects coming from math journal projects, which can lead to mini-publications and full conference publications.

If you are starting a deeper research collaboration on an existing project of your professor's, it is generally recommended that you have at least a 3.0 GPA in your mathematics courses before engaging in a significant directed research project. In particular:

  1. It is recommended that students have enrolled in (or completed) Math 2287, Foundations of Mathematics, before seeking out extended research projects.

  2. In addition, many projects may require knowledge of advanced 33XX-level or 44XX-level courses in mathematics, as well as computer programming and writing skills. However, a good mentor may be able to find some good problems for you regardless. For example, Dr. Rault can engage students who have some working knowledge of at least one of the following: linear algebra or modular arithmetic. Computer programming experience is a plus.

Can I get credit?

Yes, it may be possible to enroll in a directed study or directed research class for credit. However, this may take some additional paperwork and may increase the expectations of you in the project.

Can I get paid?

Payment in mathematics research is rare, unless you attend a summer Research Experience for Undergraduates. The university has a Career Path Internship program which can pay you to do research; course credit is another option. If your participation in the project is contingent on not working in a job, then please let Dr. Rault know so that he has a documented need and can seek further funding.

What about graduate students?

I am open to graduate students joining the team too! ISU may have funding available.

Resources